To solve this problem, we need to understand the effect of adding a constant to each observation on the standard deviation of the data set.

The standard deviation is a measure of the dispersion of a set of data points around their mean. It is calculated as follows:

\(\sigma = \sqrt{\frac{1}{N} \sum_{i=1}^{N} (x_i - \mu)^2}\)

Where:

• \(\sigma\) is the standard deviation.
• \(N\) is the number of observations.
• \(x_i\) is each individual observation.
• \(\mu\) is the mean of the observations.

When a constant is added to each observation, the mean of the data set increases by that constant. However, the deviation of each observation from the mean remains unchanged, so the difference \((x_i - \mu)\) is unaffected by the addition of the constant.

Therefore, adding a constant to every observation will not change the standard deviation. The standard deviation will remain the same as before the addition of the constant.

Given in the question, the standard deviation of the original data set is 10. Since adding 20 to each observation does not affect the standard deviation, the new standard deviation remains:

\(\text{Standard Deviation} = 10\)

Thus, the correct answer is 10.